Assessing the Impact of Uncertainties of Digital Elevation Models on Hydro-Geomorphological Analysis Using Gaussian White Noise

Digital elevation models (DEM) are mathematical representations of the Earth's bare surface in computer-readable format. The underlying measurements are often obtained by remote sensing and photogrammetry methods and processed into continuous raster data. Each of these data sources, however, provides imperfect information, and further processing steps often increase the degree of imperfection. Consequently, the process of DEM generation cumulates in uncertainty, which affects subsequent hydro- and geomorphological analyses and modelling (e.g., stream network delineation, flowpath distribution, erosion modelling).

In many DEM-based studies, however, the aspect of uncertainty related to the DEM data source has been neglected. Therefore, we propose a new approach for quantifying the effects of DEM uncertainty on hydro-geomorphological modelling based on Gaussian white noise, a concept widely used in signal processing to map noise in signals and extract the actual message context. The basic idea is to add noise to the original DEM values by means of a Gaussian distribution whose parameters are determined from the mean value of the elevation values in a moving window and the device-specific properties (precision and accuracy).

We postulate that such an approach can be used to determine uncertainties and their effect on subsequent analysis steps of hydro-geomorphological modelling. It is conceivable to create DEM ensembles depending on known parameters such as the accuracy and precision of the measuring instrument, as is used operationally in weather forecasting. Using such ensembles, probability ranges for terrain and catchment hydro-geomorphological properties can be determined and uncertainty ranges can be specified. Thus, the currently mostly deterministic approach of digital terrain modelling will be replaced by a more probabilistic understanding. Overall, our approach will help decision-makers and scientists to better assess the results of digital terrain analysis. Furthermore, it will also facilitate determining whether a result of DEM-based hydro-geomorphological analysis is sufficiently certain to answer specific research questions.